Research on what is now called quantum computing was noted by Richard Feynman. See Feynman, 1982, International Journal of Theoretical Physics 21, pp. 467-488. Feynman observed that quantum systems are inherently difficult to simulate with conventional computers but that observing the evolution of an analogous quantum system could provide an exponentially faster way to solve the mathematical model of a system. In particular, solving a model for the behavior of a quantum system commonly involves solving a differential equation related to the Hamiltonian of the quantum system. David Deutsch observed that a quantum system could be used to yield a time savings, later shown to include exponential time savings, in certain computations. If one had a problem, modeled in the form of an equation that represented the Hamiltonian of the quantum system, the behavior of the system could provide information regarding the solutions to the equation. See Deutsch, 1985, Proceedings of the Royal Society of London A 400, pp. 97-117.
A quantum bit or “qubit” is the building block of a quantum computer in the same way that a conventional binary bit is a building block of a classical computer. The conventional binary bit always adopts the values 0 and 1, which can be termed the “states” of a conventional bit. A qubit is similar to a conventional binary bit in the sense that it can adopt states, called “basis states”. The basis states of a qubit are referred to as the |0> basis state and the |1> basis state. During quantum computation, the state of a qubit is defined as a superposition of the |0> basis state and the |1> basis state. This means that the state of the qubit simultaneously has a nonzero probability of occupying the |0> basis state and a nonzero probability of occupying the |1> basis state. The ability of a qubit to have a nonzero probability of occupying a first basis state |0> and a nonzero probability of occupying a second basis state |1> is different from a conventional bit, which always has a value of 0 or 1.
Qualitatively, a superposition of basis states means that the qubit can be in both basis states |0> and |1> at the same time. Mathematically, a superposition of basis states means that the overall state of the qubit, which is denoted |ψ>, has the form|ψ>=a|0>+b|1>where a and b are coefficients respectively corresponding to probability amplitudes |a|2 and |b|2. The coefficients a and b each have real and imaginary components, which allows the phase of qubit to be modeled. The quantum nature of a qubit is largely derived from its ability to exist in a superposition of basis states, and for the state of the qubit to have a phase.
To complete a computation using a qubit, the state of the qubit must be measured (e.g., read out). When the state of the qubit is measured the quantum nature of the qubit is temporarily lost and the superposition of basis states collapses to either the |0> basis state or the |1> basis state, thus regaining its similarity to a conventional bit. The actual state of the qubit after it has collapsed depends on the probability amplitudes a and b immediately prior to the readout operation.
It has been observed that these requirements for a quantum computer are met by physical systems that include superconducting materials. Superconductivity is a phenomena that permits the flow of current without impedance, and therefore without a voltage difference. Systems that are superconducting have a superconducting energy gap that suppresses potentially decohering excitations, leading to increased decoherence times. Decoherence is the loss of the phases of quantum superpositions in a qubit as a result of interactions with the environment. Thus, decoherence results in the loss of the superposition of basis states in a qubit. See, for example, Zurek, 1991, Phys. Today 44, p. 36; Leggett et al., 1987, Rev. Mod. Phys. 59, p. 1; Weiss, 1999, Quantitative Dissipative Systems, 2nd ed., World Scientific, Singapore; Hu et al; arXiv:cond-mat/0108339, which are herein incorporated by reference in their entireties. Many superconducting structures that include Josephson junctions have been shown to support universal quantum gates. For information on universal quantum gates, see Nielsen and Chuang, Quantum Computation and Quantum Information, Cambridge University Press, 2000, as reprinted in 2002. A major challenge to the realization of scalable superconducting qubits is that the requirement for measurement often leads to coupling with decohering sources of noise. The properties of superconducting structures that permit long decoherence times serve to isolate the qubit making qubit measurement more laborious.